Cospatial σ-Hole and Lone Pair Interactions of Square-Pyramidal Pentavalent Halogen Compounds with π-Systems: A Quantum Mechanical Study

In the spirit of the mounting interest in noncovalent interactions, the present study was conducted to scrutinize a special type that simultaneously involved both σ-hole and lone pair (lp) interactions with aromatic π-systems. Square-pyramidal pentavalent halogen-containing molecules, including X-Cl-F4, F-Y-F4, and F-I-X4 compounds (where X = F, Cl, Br, and I and Y = Cl, Br, and I) were employed as σ-hole/lp donors. On the other hand, benzene (BZN) and hexafluorobenzene (HFB) were chosen as electron-rich and electron-deficient aromatic π-systems, respectively. The investigation relied upon a variety of quantum chemical calculations that complement each other. The results showed that (i) the binding energy of the X-Y-F4···BZN complexes increased (i.e., more negative) as the Y atom had a larger magnitude of σ-hole, contrary to the pattern of X-Y-F4···HFB complexes; (ii) the interaction energies of X-Y-F4···BZN complexes were dominated by both dispersion and electrostatic contributions, while dispersive interactions dominated X-Y-F4···HFB complexes; and (iii) the X4 atoms in F-I-X4···π-system complexes governed the interaction energy pattern: the larger the X4 atoms were, the greater the interaction energies were, for the same π-system. The results had illuminating facets in regard to the rarely addressed cases of the σ-hole/lp contradictory scene.


■ INTRODUCTION
Over recent decades, noncovalent interactions have been an active field of interest to the chemical and chemical-related communities. Studies on this subject have surged dramatically to interpret and rationalize findings in areas including, but not limited to, materials science and medicinal chemistry. 1−5 Understanding the nature and attitude of such interactions furnishes scientists with predictive power over complex systems encountered in everyday life. Among the essential noncovalent interactions are π-system-based interactions. The importance of such interactions is clearly manifested in a multitude of chemical and biological phenomena. 6−9 An aromatic π-system can be electron-rich or electron-deficient, as in benzene and hexafluorobenzene, respectively. However, no matter a π-system is electron-rich or electron-deficient, it can be noncovalently bonded to a σ-hole-containing molecule as in the case of halogen-containing molecule···π-system interactions. 10 The σ-hole term is assigned to the area of positive or less negative electrostatic potential emerging on the outer surface of the covalently bonded halogen, pnicogen, chalcogen, and tetrel atoms along the extension of the covalent bond. 11−14 Of all of the types of σ-hole interactions, the halogen bond is believably the most familiar and well-studied one. 15−18 The strength of halogen···π-system interaction was reported to correlate with the σ-hole magnitude of the halogen atom for the same π-system. 10 Aromatic π-systems would also participate in other interactions, including hydrogen···, tetrel···, and π-system···π-system interactions. 19−23 Over and above these types, lone pair···π-system interactions have been frequently reported. 24−28 A lone pair of electrons (simply, lone pair or lp) refers to a pair of valence electrons that are not involved in covalent bonding. Lone pairs constitute an essential aspect of Lewis structures and VSEPR theory. 29−32 Generally, the nature of lp interactions is elusive and hard to grasp, not to mention quantifying them. An eminent theory that tackled this problem and has since been widely accepted to represent electron pairs is the electron localization function (ELF). 33,34 ELF has been successfully used to visualize electrons shells and lps in a chemically intuitive way. 35−39 Curious cases of molecules that, in theory, can simultaneously engage in both lp and σ-hole interactions from the same molecular site are pentavalent halogen-bearing compounds. Lewis structure of pentavalent chlorine compounds (X-Cl-F 4 ), as displayed in Figure 1, reveals the localization of an lp on the extension of the X-Cl covalent bond. Interestingly, a positive electrostatic region (i.e., σ-hole) occurs at the same site of the lp. Such cases are problematic since the σ-hole/lp molecular site can be thought of as both an electrophilic and a nucleophilic site. Some of these compounds have indeed been studied as σ-hole donors. 40 −42 It has been reported that the halogen bonding formed by these compounds is dominantly electrostatic and dispersive in nature; while polarization plays a little role. 43 In this account, pentavalent chlorine compounds X-Cl-F 4 (where X = F, Cl, Br, and I) with C 4v symmetry will be investigated as both σ-hole and lp donors. The models will first be studied in light of molecular electrostatic potential surfaces and ELF representations. To study the σ-hole/lp···π-system interactions, potential energy surfaces (PESs) scan will be performed for X-Cl-F 4 with two aromatic π-system models namely, benzene (BZN) and hexafluorobenzene (HFB). Symmetry-adapted perturbation theory (SAPT) will be utilized to compute the contributions of different terms of the interaction energy. The study will also make use of the quantum theory of atoms in molecules (QTAIM) and noncovalent interaction index (NCI index) to analyze the noncovalent interactions in terms of the topology of electron density. The findings of the research are advantageous to the researchers who seek the chemical foundation of the ubiquitous biological and physical phenomena that involve aromatic π-system-based interactions.
■ RESULTS AND DISCUSSION MEP and ELF Representations. Molecular electrostatic potential (MEP) maps enable chemists to anticipate how a molecular site would react toward different chemical environments. 44−46 Besides, the electron localization function (ELF) is an elegant tool that helps to locate pairs of electrons, particularly lone pairs that are of deep chemical interest. 33,34 In this study, to gain such chemical perspectives for the pentavalent chlorine-containing molecules (i.e., X-Cl-F 4 ), MEP was exploited along with ELF. The geometrical structures of X-Cl-F 4 molecules were first optimized in C 4v symmetry at the MP2/aug-cc-pVDZ level of theory with PP functions added to Br and I atoms. The optimized structures are depicted in Figure S1. Based on the optimized monomers, MEPs were generated at the same level of theory and plotted on electron density contours of 0.002 au ( Figure 2).
As seen in Figure 2, a considerably large σ-hole appeared on the outer surface of the pentavalent chlorine atom along the extension of the X-Cl bond. Conspicuously, the σ-hole size was affected by the attached X atom such that the more electronwithdrawing X atom was, the larger the blue region representing the σ-hole size became ( Figure 2). Also, V s,max values decreased as the electronegativity of the X atoms decreased in the order F-Cl-F 4 > Cl-Cl-F 4 > Br-Cl-F 4 > I-Cl-F 4 with values of 52.1, 44.8, 40.4, and 33.7 kcal/mol, respectively. Consistent with the literature, these results confirmed the favorability of the considered pentavalent halogen compounds to interact as Lewis acid centers rather than Lewis base analogs. 41 Moreover, the ELF isosurface graphs ensured the existence of lone pairs at the same molecular sites of the σ-holes, a coincidence which theoretically can have a counteractive effect on the σ-hole well-known interaction ( Figure 2).
Point-of-Charge Calculations. The point-of-charge (PoC) approach has been proven as a reliable tool for quantifying the predilection of the molecular site to act as a nucleophilic or electrophilic site. 47−50 It was even proven, in some cases, where polarization was prevalent, that the PoC approach is more reliable than MEP maps. For X-Cl-F 4 ···PoC systems, molecular stabilization energies were computed in the  presence of ±0.50 au PoCs at a distance range of 2.0−7.0 Å with a step size of 0.1 Å (see the Computational Methods section for more details). The generated molecular stabilization energy graphs are displayed in Figure 3, and selected data at Cl···PoC distance of 2.5 Å are listed in Table 1.
At first glance, it was obvious that the σ-hole interaction had power over the lp interactions. This was strongly affirmed in the correlation of the σ-hole magnitude with the stabilization and destabilization energies in the case of incorporating negative and positive PoCs, respectively. For example, the molecular stabilization energies resulting from incorporating −0.50 au PoC at a Cl···PoC distance of 2.5 Å decreased (i.e., less negative) in the order F-Cl-F 4 > Cl-Cl-F 4 > Br-Cl-F 4 > I-Cl-F 4 with values of −15.05, −12.34, −10.87, and −8.70 kcal/ mol, respectively. When +0.50 au PoC was incorporated at the same Cl···PoC distance, the destabilization energy decreased (i.e., less positive) in the order F-Cl-F 4 > Cl-Cl-F 4 > Br-Cl-F 44 > I-Cl-F 4 with values of 8.93, 5.58, 3.87, and 1.43 kcal/mol, respectively.
The molecular stabilization and destabilization energies were also found to be inversely correlated with the Cl···PoC distance for the systems understudy in the presence of negative and positive PoCs, respectively ( Figure 3). However, it was observed for Br-Cl-F 4 and I-Cl-F 4 molecules that after relatively long distances, the molecules were stabilized by a positive PoC and destabilized by a negative PoC, as indicated in Figure 3. For further investigation, molecular stabilization energies in the presence of ±1.00 au PoC were also calculated at Cl···PoC distance of 2.5 Å, and the results are presented in Table 1. As seen in Table 1, when +1.00 au PoC was incorporated, Br-Cl-F 4 and I-Cl-F 4 exhibited stabilization energies of −1.09 and −6.12 kcal/mol, respectively. While this could be attributed to the negative fluorine atoms interactions, the lp might also have accounted for some part of the attractive interaction. Possibly, competition occurred between the electrophilicity of the σ-hole on one side and the nucleophilicity of the lone pair and fluorine atoms on the other side such that each side overwhelmed the other at a certain range of distance or different values of PoC. On the other hand, when a large negative value of PoC (i.e., −1.00 au) was used at a Cl···PoC distance of 2.5 Å, it resulted in more stabilized molecules in the order F-Cl-F 4 > Cl-Cl-F 4 > Br-Cl-F 4 > I-Cl-F 4 with stabilization energies values of −35.46, −30.70, −28.04, and −24.06 kcal/mol, respectively. This was consistent with the results obtained in the case of −0.50 au PoC.
To better conceive the situation, MEPs of the monomers were generated in the presence of ±1.00 au PoCs and are depicted in Figure S2. As obvious in Figure S2, PoC with a value of +1.00 au could induce negative electrostatic potential regions that replaced the positive σ-hole. It was obvious also that the size of the negative region correlated with the size of the X attached atom in X-Cl-F 4 monomers in the order I-Cl-F 4 > Br-Cl-F 4 > Cl-Cl-F 4 > F-Cl-F 4 . The emerging negative electrostatic potential region could interpret the stabilization energy values for Br-Cl-F 4 and I-Cl-F 4 when +1.00 au PoC was inserted.
PES Scan. While σ-hole···π-system and lp···π-system interactions have been widely investigated, 8,51−53 cases of combined σ-hole/lp interaction with π-systems received no such consideration. To address this case, σ-hole/lp···π-system interactions were examined using X-Cl-F 4 complexes with BZN and HFB as an electron-rich and electron-deficient π-systems, respectively. Potential energy surface (PES) scan at the MP2/ aug-cc-pVDZ(PP) level of theory was performed on X-Cl-F 4 ···π-system complexes in C 2v symmetry (see Figure 1) at a  distance range from 2.5 to 7.0 Å with a step size of 0.1 Å. PES scan graphs are depicted in Figure 4, and the computed binding energies at the most favorable Cl···π-system distance are presented in Table 2.
According to the data displayed in Figure 4, all of the studied σ-hole/lp···π-system interactions exhibited significant negative binding energies. This revealed that the pentavalent chlorinebearing systems had the capacity to preferentially interact with both electron-rich and electron-deficient π-systems. From Table 2, the MP2/aug-cc-PVTZ(PP) binding energies showed very close values to the MP2/aug-cc-PVDZ(PP) counterparts, ensuring the adequacy of the implemented level of theory. Quantitatively speaking, as shown in Table 2, the binding energies for X-Cl-F 4 ···BZN complexes decreased (i.e., became less negative) in the order F-Cl-F 4 ··· > Cl-Cl-F 4 ··· > Br-Cl-F 4 ··· > I-Cl-F 4 ···BZN with values of −6.80, −6.56, −6.34, and −6.03 kcal/mol, respectively. This was understandable recalling the order of V s,max of the X-Cl-F 4 monomers. For the electrondeficient HFB complexes, the pattern was reversed such that the binding energy increased in the order F-Cl-F 4 ··· < Cl-Cl-F 4 ··· < Br-Cl-F 4 ··· < I-Cl-F 4 ···HFB with values of −3.50, −4.43, −4.71, and −5.10 kcal/mol, respectively. In contrast to the V s,max pattern, the obtained energetic results could be ascribed to the successive diminution of the repulsive forces between the electron-deficient regions within the X-Cl-X 4 ···HFB complexes. While this seems, ostensibly, reasonable due to the positivity of HFB and the increasing positivity of the σhole, previous studies of σ-hole interactions with HFB found that the binding energy of σ-hole-containing molecule···HFB complexes correlated with the value of V s,max of the interacting σ-hole, 10 which was not the case here. It was inferred that other factors besides the σ-hole interaction had affected the binding energy pattern.
SAPT Analysis. Symmetry-adapted perturbation theory (SAPT) is presumably the most familiar and widely used approach among energy decomposition analysis (EDA) methodologies. 54 SAPT breaks down the binding energy into its constituents, which means it analyzes the binding energy into its electrostatic (E elst ), dispersion (E disp ), induction (E ind ), and exchange (E exch ) components. 55 For the studied complexes, SAPT analysis was carried out at the SAPT2 + (CCD)δMP2 level of truncation, and the results are summarized in Table 3.
For X-Cl-F 4 ···HFB complexes, E elst values decreased significantly, and the noncovalent interactions were dominated by dispersion forces. This might entail that attractive interaction is directed by the σ-hole rather than the lone pair. If the interaction had been directed by the lone pair, the electrostatic term would have, supposedly, increased by . Binding energies calculated at the MP2/aug-cc-pVDZ(PP) level of theory for X-Cl-F 4 ···π-system complexes (where X = F, Cl, Br, and I; π-system = benzene (BZN) and hexafluorobenzene (HFB)) at a Cl···π-system distance of 2.5−7.0 Å with a step size of 0.1 Å. Table 2. Binding Energies (in kcal/mol) Calculated at the MP2/aug-cc-pVDZ(PP) and MP2/aug-cc-pVTZ(PP) Levels of Theory for X-Cl-F 4 ···π-System Complexes (Where X = F, Cl, Br, and I; π-System = Benzene (BZN) and Hexafluorobenzene (HFB)) at the Most Favorable Cl···π-System Distance The most favorable X-Cl-F 4 ···π-system distance based on PES scan illustrated in Figure 4. b PP functions were added to Br and I atoms.
ACS Omega http://pubs.acs.org/journal/acsodf Article decreasing the electron-richness of the π-systems. As seen in  Table 3 that the values of E exch for X-Cl-F 4 ···BZN complexes are higher (i.e., more positive) than those of their counterparts in X-Cl-F 4 ···HFB complexes. For example, E exch was 10.18 and 7.92 kcal/mol for F-Cl-F 4 ··· BZN and F-Cl-F 4 ···HFB, respectively. This entailed that the Pauli repulsion in the electron-rich BZN complexes was greater than that of the electron-deficient HFB complexes. Assumedly, the Pauli repulsion between the lone electron pair of X-Cl-F 4 monomers and the π-system cloud of BZN was higher (i.e., more positive) than the repulsion between the same lone pair and the electron-deficient π-system cloud of HFB.
QTAIM Analysis. Despite being frequently called into question, 56−64 the quantum theory of atoms in molecules (QTAIM) is routinely used to visualize and quantify chemical bonding between atoms. 65−69 The theory is fundamentally based on the topological analysis of electron density. Through electron density analysis, bond paths (BPs) were identified and bond critical points (BCPs) were located. Moreover, the characteristics of BCPs were calculated. These characteristics include electron density (ρ b ), Laplacian of the electron density (∇ 2 ρ b ), and total energy density (H b ). For the studied complexes, QTAIM analysis was performed, and the QTAIM molecular graphs are depicted in Figure 5. BCPs characteristics were calculated and are indicated in Table 4.
In general, six bond paths arose between the pentavalent chlorine atom of the X-Cl-F 4 molecule and the carbon atoms of the π-system in F-Cl-F 4 ···BZN and ···HFB complexes ( Figure  5). It was noted in the case of Cl-Cl-F 4 ···, Br-Cl-F 4 ···, and I-Cl-F 4 ···BZN complexes that additional two bond paths formed between two fluorine atoms and the two facing carbon atoms of the benzene ring.
Considering BCPs characteristics, tabulated in Table 4, relatively small values of ρ b accompanied by positive values of both H b and ∇ 2 ρ b were noted, indicating the closed-shell nature of the examined interactions. Moreover, a general correlation was found between the binding energies of the X-Cl-F 4 ···BZN complexes with the ρ b , ∇ 2 ρ b values. For instance, the values of ρ b were 0.00701, 0.00655, 0.00641, and 0.00636 au for F-Cl-F 4 ···, Cl-Cl-F 4 ···, Br-Cl-F 4 ···, and I-Cl-F 4 ···BZN complexes with binding energies of −6.80, −6.56, −6.34, and −6.03 kcal/mol, respectively. For X-Cl-F 4 ···HFB complexes, the ρ b and ∇ 2 ρ b patterns were a bit distorted, but, even though, still a correlation between ρ b on one side and the binding energies on the other side could be noted. In addition, H b and ∇ 2 ρ b values of X-Cl-F 4 ···HFB complexes correlated obviously with the binding energies. For example, H b values were found to be 0.00089, 0.00096, 0.00098, and 0.00104 au for F-Cl-F 4 ···, Cl-Cl-F 4 ···, Br-Cl-F 4 ···, and I-Cl-F 4 ···HFB complexes, respectively.
NCI Analysis. While QTAIM adheres to stringent criteria for indicating chemical bonding between atoms, the noncovalent interaction (NCI) index adopts more flexible measures to identify long-range chemical bonding. 70 Hence, NCI analysis occasionally manages to spot regions of chemical bonding that are not present in the QTAIM picture. 10,71 NCI index makes use of the reduced density gradient (RDG) quantity to reveal regions of both attractive and repulsive interaction. Basically, NCI exploits the quantity sign(λ 2 )ρ (where λ 2 is the second eigenvalue of the Hessian matrix and ρ is the electron density) to determine whether the interaction is attractive or repulsive and to give a measure of its strength. For the studied complexes, NCI molecular graphs were generated and are displayed in Figure 6.
NCI graphs disclosed the occurrence of the X-Cl-F 4 ···πsystem interactions between pentavalent chlorine and the πsystem, which was consistent with the QTAIM analysis. However, NCI molecular graphs unveiled additional bonding between the four coplanar fluorine atoms in the X-Cl-F 4 molecule and the π-system. It was perceived that the binding energy pattern of X-Cl-F 4 ···HFB complexes could be justified by the F 4 contribution to the bonding between the two interacting monomers. Apparently, the bonding between the Table 3. Electrostatic (E elst ), Dispersion (E disp ), Induction (E ind ), and Exchange (E exch ) Interactions Contributions to the Binding Energies of X-Cl-F 4 ···π-System Complexes (Where X = F, Cl, Br, and I; π-System = Benzene (BZN) and Hexafluorobenzene (HFB)) Based on the Symmetry-Adapted Perturbation Theory (SAPT) Analysis  . QTAIM diagrams of X-Cl-F 4 ···π-system complexes (where X = F, Cl, Br, and I; π-system = benzene (BZN) and hexafluorobenzene (HFB)). The red and yellow dots indicate the locations of bond critical points and ring critical points between the monomers at the most favorable Cl···π-system distance, respectively.

ACS Omega
http://pubs.acs.org/journal/acsodf Article negative F 4 in X-Cl-F 4 and the positive carbon atoms in HFB increased as the F 4 became more negative, which happened when the X atom was less electron-withdrawing. This also could be related to the increase of the electrostatic terms E elst (see the SAPT Analysis section) as less electron-withdrawing X atom was attached to the pentavalent chlorine atom. Hence, it could be concluded that the coplanar F 4 interactions in X-Cl-F 4 ···HFB complexes had superiority over the σ-hole interaction of the pentavalent chlorine atom. In the next section, to broaden the scope of the study, the concepts deduced previously will be introduced to other pentavalent halogen atoms to assess the validity and generality of these concepts.
Other Pentavalent Halogens. To adequately generalize the study to other pentavalent halogens, the interactions of F-Br-F 4 and F-I-F 4 were studied. All of the quantum chemical treatments used previously were applied to F-Br-F 4 and F-I-F 4 with the same methodology. This included optimization ( Figure S3), MEP, and ELF representation ( Figure S4), PoC ( Figure S5, Table S1). For the sake of systemization, F-Y-F 4 (where Y = Cl, Br, and I) behaviors were evaluated and compared to each other.
Generally, the findings were consistent with the previously obtained results. The optimization of F-Y-F 4 monomers resulted in semisquare-pyramidal structures ( Figure S3). According to the data displayed in Figure S4, the coincidence (and coexistence) of the σ-hole and the lone pair of the Y atom was plainly observed. It was also, expectedly, noted that V s,max correlated with the size of the halogen atom. Numerically, V s,max had values of 52.1, 65.5, and 70.0 kcal/mol for F-Cl-F 4 , F-Br-F 4 , and F-I-F 4 , respectively.
The binding energies of F-Y-F 4 ···BZN complexes clearly correlated with the V s,max of the Y atom's σ-hole, while the binding energies of F-Y-F 4 ···HFB inversely correlated with V s,max . From the data given in Table 5, the binding energies of F-Y-F 4 ···BZN complexes were −6.80, −9.04, and −10.67 kcal/ mol for Y = Cl, Br, and I, respectively. Evidently, a salient similarity was noted for the computed binding energies at the MP2/aug-cc-pVDZ(PP) and MP2/aug-cc-pVTZ(PP) levels of theory. These results support previous researches that have examined the interactions within the pentavalent halogenbased complexes. 72,73 For F-Y-F 4 ···HFB complexes, the binding energies were −3.50, −3.23, and −2.04 kcal/mol for F-Cl-F 4 ···, F-Br-F 4 ···, and F-I-F 4 ···HFB complexes, respectively. SAPT analysis of the complexes was performed at the SAPT2 + (CCD)MP2 level of theory and the results are depicted in Table S2. Table S2 shows the domination of E elst and E disp in F-Y-F 4 ··· BZN complexes, while E elst dropped significantly in F-Y-F 4 ··· HFB complexes. Besides, E exch terms of F-Y-F 4 ···BZN complexes were higher than their counterparts in F-Y-F 4 ··· HFB complexes, assumingly due to the electron-richness of BZN and electron-deficiency of HFB. For example, E elst , E disp , E ind , and E exch of F-I-F 4 ···BZN complex were −11.67, −10.87, −6.72, and 17.87 kcal/mol, respectively, while the values for F-I-F 4 ···HFB complex were 0.38, −7.63, −3.34, and 8.03 kcal/ mol, respectively. Finally, E elst correlated with V s,max of the Y atom in F-Y-F 4 ···BZN complexes, and inversely correlated with V s,max of the Y atom in F-Y-F 4 ···HFB complexes. As shown in Table S2, E elst was −6.39, −8.80, and −11.67 kcal/mol for F-Cl-F 4 ···, F-Br-F 4 ···, and F-I-F 4 ···BZN, respectively, and it was −1.55, −0.81, and 0.38 kcal/mol for F-Cl-F 4 ···, F-Br-F 4 ···, and F-I-F 4 ···HFB, respectively. It is noteworthy that the SAPT results obtained for F-Y-F 4 ···BZN complexes are consistent with a previous study in having relatively high Pauli repulsion terms with considerably large electrostatic and dispersion interaction terms. 74 Regarding QTAIM and NCI analyses, QTAIM and NCI molecular graphs of F-Y-F 4 ···π-system complexes were generally similar to those of X-Cl-F 4 ···π-system complexes ( Figures S6 and S7). Looking at Figure S6, the QTAIM analysis showed six noncovalent bond critical points associated with six bond paths between the Y atom in F-Y-F 4 and the carbon atoms of the π-system. The NCI molecular graphs confirmed the bonding between the Y atom and the π-system ( Figure S7), but they exhibited additional bonding between the F 4 atoms in F-Y-F 4 and the π-system. The mentioned bonding, as evidenced by RDG isosurfaces sizes, was weaker as the size of the Y atom was larger. It could be reasoned that the binding energy pattern of F-Y-F 4 ···HFB complexes was notably affected by the F 4 interactions with the carbon atoms of HFB. As seen in Figure S7, the RDG isosurface had the largest size in the F-Cl-F 4 ···HFB complex and diminished in F-Br-F 4 ···HFB until it entirely disappeared in the F-I-F 4 ···HFB complex. So, as in the case of X-Cl-F 4 ···HFB complexes, the interactions of the Table 5. Binding Energies (in kcal/mol) Calculated at the MP2/aug-cc-pVDZ(PP) and MP2/aug-cc-pVTZ(PP) Levels of Theory for F-Y-F 4 ···π-System Complexes (Where Y = Br and I; π-System = Benzene (BZN) and Hexafluorobenzene (HFB)) at the Most Favorable Y···π-System Distance The most favorable F-Y-F 4 ···π-system distance based on PES scan (Figure 7). b PP functions were added to Br and I atoms. To validate this point, the next section is dedicated to investigating the effect of replacing F 4 atoms in the F-I-F 4 ···πsystem complexes with Cl 4 , Br 4 , and I 4 atoms on the binding energy.
F-I-X 4 ···π-System Complexes. To assess the role of X 4 atoms in F-I-X 4 ···π-system complexes, where X = F, Cl, Br, and I, PES scans were executed at the MP2/aug-cc-pVDZ level of theory (with PP functions added to Br and I atoms) in the distance ranging from 2.5 to 7.0 Å between the central I atom and the centroid of the π-system with a step size of 0.1 Å. The curves of the PES scan are given in Figure 8, and the binding energies of the F-I-X 4 ···π-system complexes at the most favorable I···π-system distance are presented in Table 6.
As can be seen from Table 6, the binding energy increased (i.e., more negative) as the size of the X 4 atoms increased. Intelligibly, the larger and, consequently, the more polarizable the X atom was, the more capable it was to form a stronger noncovalent bond. Hence, the resulting binding energies correlated with the size of X 4 atoms. The larger and, consequently, the less electron-withdrawing the X atom was, the smaller the V s,max value of the central iodine atom's σ-hole. This may plausibly imply that the interactions of the circumferential atoms around the σ-hole-containing atom are so influential to the extent that they may surpass the interaction of the σ-hole itself.

■ CONCLUSIONS
To inquire into the very nature of the pentavalent halogen atoms interactions, the pentavalent halogens were investigated as both σ-hole and lone pair (lp) donors. Molecular electrostatic potential (MEP) and electron localization function (ELF) graphs of X-Cl-F 4 and F-Y-F 4 (where X = F, Cl, Br, and I and Y = Cl, Br, and I) demonstrated the coincidence of the σ-hole and the lone pair at the same molecular site. The PoC approach revealed the domination of the σ-hole interaction over the lp interaction. The interactions of X-Cl-F 4 and F-Y-F 4 with benzene (BZN) and hexafluorobenzene (HFB) were studied by means of potential energy surface (PES) scan, symmetry-adapted perturbation theory (SAPT), the quantum theory of atoms in molecules (QTAIM), and noncovalent interaction (NCI) index. The results revealed that: (i) the binding energies of X-Cl-F 4 ··· and F-Y-F 4 ···BZN complexes increased (i.e., more negative) as the V s,max of the σ-hole of the Cl/Y atom increased while the binding energies of X-Cl-F 4 ··· and F-Y-F 4 ···HFB complexes decreased as the V s,max of the σ-hole of the Cl/Y atom increased; (ii) the interactions of X-Cl-F 4 ··· and F-Y-F 4 ···BZN complexes were dominated by both dispersion and electrostatic contribution while for X-Cl-F 4 ···, and F-Y-F 4 ···HFB complexes the interactions were dominated by dispersion terms only; (iii) the exchange interaction (Pauli repulsion) in X-Cl-F 4 ··· and F-Y-F 4 ···BZN complexes was larger (i.e., more positive) than that of X-Cl-F 4 ··· and F-Y-F 4 ···HFB complexes; (iv) NCI analysis justified the binding energy pattern of X-Cl-F 4 ··· and F-Y-F 4 ···HFB complexes as it uncovered the interactions between the negative F 4 atoms and the positive HFB carbon atoms; (v) when substituting the X 4 atoms in F-I-X 4 ···π-system complexes with larger and more polarizable halogen atoms, the interaction energy was found to increase as larger X atoms were attached. The findings contain data and trends that can be beneficial to many chemical-related research domains.
Computational Methods. In this study, the squarepyramidal X-Cl-F 4 model was chosen as a simultaneously σhole and lp donor (where X = F, Cl, Br, and I). Benzene (BZN) and hexafluorobenzene (HFB) were selected as electron-rich and electron-deficient aromatic π-systems, respectively. First, X-Cl-F 4 monomers were optimized at the MP2/aug-cc-pVDZ level of theory, 75,76 with PP functions added to Br and I atoms. 77 Molecular electrostatic potential (MEP) maps were generated for all X-Cl-F 4 monomers on electron density isosurfaces of 0.002 au. 78 The maximum value of positive electrostatic potential (V s,max ) was extracted using Multiwfn software 3.7 79 along with the ELF molecular graphs.
The point-of-charge (PoC) approach was employed to examine the nucleophilicity or electrophilicity character of the σ-hole/lp donor in the pentavalent X-Cl-F 4 molecules. 47−50 This was achieved by evaluating the molecular stabilization energies of the monomers in the presence of −0.50 and + 0.50 au PoC, within a halogen···PoC distance ranging from 2.0 to 7.0 Å with a step size of 0.1 Å. The molecular stabilization energy (E stabilization ) was quantified as follows: 80 For X-Cl-F 4 ···π-system complexes, the optimized monomers were positioned such that C 2v symmetry of the complexes was maintained (see Figure 1). This was to allow the occurrence of the desired interaction between the σ-hole/lp donor and the centroid of the π-system. Potential energy surface (PES) scans were then performed on the studied complexes in a distance ranging from 2.5 to 7.0 Å between the σ-hole/lp donor atom and the centroid of the π-system with a step size of 0.1 Å. The The most favorable F-I-X 4 ···π-system distance based on PES scan illustrated in Figure 8. b PP functions were added to Br and I atoms.
ACS Omega http://pubs.acs.org/journal/acsodf Article binding energies were computed at the MP2/aug-cc-pVDZ-(PP) level of theory. The basis set superposition error (BSSE) was eliminated via the counterpoise correction method. 84 The binding energies were also estimated at the MP2/aug-cc-pVTZ(PP) level of theory for the investigated complexes at the most favorable X-Cl-F 4 ···π-system distance based on the PES scan. Geometrical optimization, MEP analysis, and all energy calculations were executed using Gaussian09 software. 85 Furthermore, symmetry-adapted perturbation theory-based energy decomposition analysis (SAPT-EDA) of the binding energies was performed at the SAPT2 + (CCD)δMP2 level of theory 86−88 using PSI4 software. 89 The SAPT binding energy was estimated as the sum of the electrostatic interaction (E elst ), dispersion interaction (E disp ), induction or polarization interaction (E ind ), and the exchange interaction (E exch ) according to the following equation Quantum theory of atoms in molecules (QTAIM) and noncovalent interaction (NCI) index analyses were also performed at the MP2/aug-cc-pVDZ(PP) level of theory to elucidate the nature of the investigated interactions. 90,91 Bond critical points (BCPs) and their characteristics were computed by means of Multiwfn 3.7 software. 79 Both QTAIM and NCI molecular graphs were visualized using Visual Molecular Dynamics (VMD) software. 92 To assess the generality of the obtained results, the study was extended to involve other pentavalent halogen-containing molecule···π-system interactions. In that extension, all of the quantum chemical calculations mentioned before were carried out for F-Br-F 4 ···π-system and F-I-F 4 ···π-system complexes. Finally, the effect of substituting the X 4 atoms with more polarizable halogens in the F-I-X 4 ···π-system complexes was explored. This was attained by computing the binding energies of F-I-Cl 4 ···, F-I-Br 4 ···, and F-I-I 4 ···π-system complexes and comparing the results to those of F-I-F 4 ···π-system complexes.
Optimized geometries of X-Cl-F 4 and F-Y-F 4 monomers; MEP maps of X-Cl-F 4 monomers in the presence of ±1.00 au PoC; MEP, ELF, and PoC calculations of F-Y-F 4 monomers; and SAPT calculations, QTAIM and RDG-NCI molecular graphs of F-Y-F 4 ···π-system complexes (PDF)